Réponse:
Bonsoir,
1)
A(x)= (x+2)(2x+3)
A(x)= 2x²+3x+4x+6
A(x)= 2x²+7x+6
B(x)= (2x-3)² ---> IR: (a-b)²= a²-2ab+b²
B(x)= (2x)²-2*2x*3+3²
B(x)= 4x²-12x+9
C(x)= (5x-3)(2x+4)-(5x-3)(3x-2)
C(x)= (5x-3)(2x+4)-(5x-3)(3x-2)
C(x)= (5x-3)(2x+4-3x+2)
C(x)= (5x-3)(-x+6)
D(x)= (3x+1)²-(4x+1)²--> IR: a²-b²=(a-b)(a+b)
D(x)= (3x+1-(4x+1)) (3x+1+(4x+1))
D(x)= (-x)(7x+2)
D(x)=-7x²-2x
Ou
D(x)= (3x+1)²-(4x+1)² -->IR: (a+b)²= a²+2ab+b²
D(x)= [(3x)²+6x+1²] - [(4x)²+8x+1²]
D(x)= (9x²+6x+1) - (16x²+8x+1)
D(x)= -7x²-2x
2)
A(x)= 3(x-5)²+ (x-5)(2x+1)
A(x)= 3(x+5)(x-5)+(x-5)(2x+1)
A(x)= (3x-15)(x-5)+(x-5)(2x+1)
A(x)= (x-5)(3x-15+2x+1)
A(x)= (x-5)(5x-14)
B(x)=4x²-1
B(x)= (2x)²-1² --> IR: a²-b²= (a-b)(a+b)
B(x)= (2x-(-1)) (2x+(-1))
B(x)= (2x+1) (2x-1)
C(x)= (3x-4)² + 5(4-3x)
C(x)= (3x-4)² -5(3x-4)
C(x)= (3x-4)(3x-4)-5(3x-4)
C(x)= (3x-4)(3x-4-5)
C(x)= (3x-4)(3x-9)
D(x)= x²-2x+1
D(x)= x²-2x+1² -->IR: a²-2ab+b²-->(a-b)²
D(x)= (x-1)²
F(x)= (2x+3)²-(5x-1)² IR: a²-b²= (a-b)(a+b)
F(x)= (2x+3-(5x-1)) (2x+3+(5x-1))
F(x)= (2x+3-5x+1) (2x+3+5x-1)
F(x)= (-3x+4) ( 7x+2)
Je vous laisse continuer, je vous remet les identités remarquables dans les explications.
Bonne fin de soirée.
Explications étape par étape:
IR= identité remarquable
1.(a+b)²= a²+2ab+b²
2.(a-b)²= a²-2ab+b²
3.a²-b²= (a-b)(a+b)
